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Isomorphism of intersection and union types†

Published online by Cambridge University Press:  07 August 2015

MARIO COPPO ,
MARIANGIOLA DEZANI-CIANCAGLINI ,
INES MARGARIA  and
MADDALENA ZACCHI
MARIO COPPO
Affiliation:
Dipartimento di Informatica, via Pessinetto 12, 10131 Torino, Italy Email: coppo@di.unito.it, dezani@di.unito.it, ines@di.unito.it, zacchi@di.unito.it
MARIANGIOLA DEZANI-CIANCAGLINI
Affiliation:
Dipartimento di Informatica, via Pessinetto 12, 10131 Torino, Italy Email: coppo@di.unito.it, dezani@di.unito.it, ines@di.unito.it, zacchi@di.unito.it
INES MARGARIA
Affiliation:
Dipartimento di Informatica, via Pessinetto 12, 10131 Torino, Italy Email: coppo@di.unito.it, dezani@di.unito.it, ines@di.unito.it, zacchi@di.unito.it
MADDALENA ZACCHI
Affiliation:
Dipartimento di Informatica, via Pessinetto 12, 10131 Torino, Italy Email: coppo@di.unito.it, dezani@di.unito.it, ines@di.unito.it, zacchi@di.unito.it
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Abstract

This paper gives a complete characterisation of type isomorphism definable by terms of a λ-calculus with intersection and union types. Unfortunately, when union is considered the Subject Reduction property does not hold in general. However, it is well known that in the λ-calculus, independently of the considered type system, the isomorphism between two types can be realised only by invertible terms. Notably, all invertible terms are linear terms. In this paper, the isomorphism of intersection and union types is investigated using a relevant type system for linear terms enjoying the Subject Reduction property. To characterise type isomorphism, a similarity between types and a type reduction are introduced. Types have a unique normal form with respect to the reduction rules and two types are isomorphic if and only if their normal forms are similar.

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Information
Mathematical Structures in Computer Science , Volume 27 , Special Issue 5: Computing with Lambda-terms. A Special Issue Dedicated to Corrado Böhm for his 90th Birthday , June 2017 , pp. 603 - 625
Copyright
Copyright © Cambridge University Press 2015 

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Footnotes

†

Dedicated to Corrado Böhm on the occasion of his 90th Birthday.

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